76 Derive each of the following answers using appropriate interest table or interest formula Show your derivations clearly a) Consider the following cash flow diagram. P is the unknown amount of deposit that is required to generate the four annual withdrawals. Given the varying interest rates in the digram, what is the amount of the deposit? Show your cakulations clearly. $1.500 $2.000 $3.000 SIMO 8% - 10%- 6%- b) On her 31" birthday, Sapphine invests $1,000 into her employer's retirement plan, and she continues to make annual $1,000 payments for 10 years. So, her total contribution (ie. principal) is $10,000. After making these 10 annual payments, Sapphine then stops making payments into her plan and keeps her money in the savings plan untouched for 25 more years. On the other hand, Peter starts putting money aside on his 41" birthday when he deposits $1,000, and continues these payments until he gets to be 65 years old. Peter's contributed principal amounts to $25,000 over this period of time. If Sapphine's and Peter's retirement plans carn interest of 6% per year, how much will they have accumulated (principal plus interest) when they reach 65 years old? c) Suppose the interest rate is 10%. Calculate the equivalent annual cost of the machine described in the following table. S100.000 Inital cost Estimated life Salvage value Other costs 25 years S25.000 $15,000 per year for the first 15 years $20,000 per year for the next 10 years